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Sergeu [11.5K]
2 years ago
8

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The d

istribution of the number of daily requests is bell-shaped and has a mean of 61 and a standard deviation of 11. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 61 and 94?
Mathematics
1 answer:
zaharov [31]2 years ago
5 0

Answer:

P(61≤ X≤94) = 49.85%

Step-by-step explanation:

From the given information:

The mean of the bell shaped fluorescent light bulb μ = 61

The standard deviation σ = 11

The objective of this question is to determine the approximate percentage of light bulb replacement requests numbering between 61 and 94 i.e P(61≤ X≤94)

Using the empirical (68-95-99.7)rule ;

At 68% , the data lies between  μ - σ and μ + σ

i.e

61 - 11 and 61 + 11

50 and 72

At  95%, the data lies between  μ - 2σ and μ + 2σ

i.e

61 - 2(11) and 61 + 2(11)

61 - 22 and 61 +22

39   and   83

At 99.7%, the data lies between  μ - 3σ and μ + 3σ

i.e

61 - 3(11) and 61 + 3(11)

61 - 33 and 61 + 33

28   and   94

the probability equivalent to 94 is when  P(28≤ X≤94) =99.7%

This implies that ,

P(28≤ X≤94) + P(61≤ X≤94) = 99.7%

P(28≤ X≤94) = P(61≤ X≤94) = 99.7 %    

This is so because the distribution is symmetric about the mean

P(61≤ X≤94) = 99.7 %/2

P(61≤ X≤94) = 49.85%

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pychu [463]

Given:

The figure of a rhombus QRST.

To find:

A. The value of x.

B. The measure of angle RQP.

Solution:

A. We need to find the value of x.

We know that the diagonals of a rhombus are perpendicular bisectors. It means the angles on the intersection of diagonals are right angles.

m\angle RPS=90^\circ                       [Right angle]

(5x+15)^\circ=90^\circ

(5x+15)=90

5x=90-15

5x=75

Divide both sides by 5.

x=\dfrac{75}{5}

x=15

Therefore, the value of x is 15.

B. We need to find the measure of angle RQP.

From the given figure, it is clear that

m\angle RQP=(2x+3)^\circ

Putting x=15, we get

m\angle RQP=(2(15)+3)^\circ

m\angle RQP=(30+3)^\circ

m\angle RQP=33^\circ

Therefore, the measure of angle RQP is 33 degrees.

8 0
2 years ago
Determine the equation of the line that passes through A(2,-5) and B(6,-3).
yaroslaw [1]

Answer:

y = 1/2x - 6

Step-by-step explanation:

y2 - y1 / x2 - x1

-3 - (-5) / 6 - 2

2/4

= 1/2

y = 1/2x + b

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2 years ago
Please solve equations by completing square
BlackZzzverrR [31]
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3 years ago
Six less than two times a number is no more than 7
ziro4ka [17]

Answer:

n <=6.5

Step-by-step explanation:

Six less than two times a number is no more than 7

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Add 6 to each side

2n-6+6 <=7+6

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3 years ago
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DaniilM [7]
Answer: 1 ton

Step-By-Step-Explanation:
8 0
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